length of a Bezier curve in 3D

Mathematics, theory and usage in algorithm construction
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Yoshi
Posts: 16
Joined: Fri Jun 30, 2023 11:03 pm

length of a Bezier curve in 3D

Post by Yoshi »

Any idea how to calculate the length of a Bezier curve in 3D? Suppose I know three control points [x1,y1,z1] , [x2,y2,z2] and [x3,y3,z3]...
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venhard
Posts: 6
Joined: Tue Jul 04, 2023 6:52 am

Re: length of a Bezier curve in 3D

Post by venhard »

hi, there is a book about it. This is full with math and examples. I have a PDF copy. I send this to you.
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rector
Posts: 2
Joined: Tue Jul 04, 2023 10:01 pm

Re: length of a Bezier curve in 3D

Post by rector »

There exists 3d Bezier.class in PHP which is defined by three points and returns curve length. I am unable to attach the file here. Send PM.
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tamagotchi
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Joined: Fri Jul 07, 2023 11:41 am

Re: length of a Bezier curve in 3D

Post by tamagotchi »

yoshi, check this on wikipedia: https://en.wikipedia.org/wiki/Composite ... zier_curve Now, assume the control points of Eight-segment quadratic polybezier have different "Z"-coordinates. This results in flat curved circle. The question is, how to calculate the perimeter and area from eight control points, each defined by three coordinates {x1, y1, z1] .... [x8, y8, z8]
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Yoshi
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Re: length of a Bezier curve in 3D

Post by Yoshi »

venhard, thank you for book posting
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